\section{Insurer Risk And Surplus Requirements}
\label{sec:SurplusRequirements}

I have shown that small insurers have higher probabilities, of high operating losses, than large insurers, a consequence capitation advocates must have failed to consider because this alone shows that capitation cannot work in efficient health care (finance) systems. 

All insurers must anticipate years in which their PLREs exceed 0.8500. If they incur PLREs higher than 0.8500 and have no additional assets (Surplus\index{Surplus}), beyond current premiums, they become insolvent (bankrupt). Insolvency means failed commitments to suppliers, employees, stockholders, claimants, and policyholders. Regulators set many solvency requirements, including: minimum capitalization, statutory surplus and reserve requirements; rate regulation; restrictions on risky investments; and also conduct periodic financial inspections to reduce the numbers of insurer insolvencies \citep{Barth2000, Cummins1994}.

\subsection{Solvency Preserving Loss Ratios}
\label{sec:SolvencyPreservingLossRatio}

There are no magic formulas for solvency protection. I require all insurers to meet a uniform solvency protection standard, defined by the ``Solvency Preserving Loss Ratio\index{Solvency Preserving Loss Ratio}'' ($SPLR_N$\index{SPLR}). $SPLR_N$\index{$SPLR_N$} is the highest level PLRE insurers must be able to cover, before issuing policies, and it protects each insurer from PLREs up to PLR + 3 * $\sigma_{e_{I}}$. Each insurer will be able to cover all the claims costs it incurs with probability 0.9987. Insurers with adequate Surplus face insolvency less than 14 out of 10,000 years. 

Table~\ref{tab:InsurerOperatingResultsByPortfolioSize} Row 8, shows insurers' Solvency Preserving Loss Ratios. $SPLR_{PI}$ = 0.9000, but larger insurers, with lower standard errors, have lower SPLRs: $SPLR_{NHI} = 0.75855$ and  $SPLR_{B} = 0.79743$, while smaller insurers, with higher standard errors, have much higher SPLRs: $SPLR_{D} = 1.22434$ and $SPLR_{E} = 2.25000$. To be as well prepared as $PI$, to cover unusually high claims costs, $D$ and $E$ need to set aside huge amounts of liquid assets, before issuing any policies. these uniform risk adjusted surplus requirements inhibit market entry by small, inefficient insurers, that are likely to fail, and encourage market entry by large, efficient insurers that are likely to succeed.

Regulators encourage other insurers to cover failed insurer's policies to maintain consumer confidence. $NHI$ and $B$, with profits over 9\%, and 5\%, can cover many failed insurers' policies and earn good will. But small, inefficient insurers decrease the  efficiency of insurance markets, taking excessive profits, or shifting their losses, to other insurers. 

\subsection{Surplus Requirements By Portfolio Size}
\label{sec:SurplusRequirementsByPortfolioSize}

Insurer's surplus\index{Surplus} requirements, \textbf{${S_N}$}\index{$S_N$}, are the dollar amounts of highly liquid assets, they must set aside before issuing policies, to cover the layer of operating losses between PLREs of 0.8500 and $SPLR_{N}$ [i.e. $S_{N}$ = Max(0,($SPLR_{N}$ - 0.8500) * Earned Premiums * Size)].  Table~\ref{tab:InsurerOperatingResultsByPortfolioSize} Row 9 shows that $S_{NHI}$ = $S_{B}$ = \$0.00 because $\Phi_{NHI}$(0.8500) = $\Phi_{B}$(0.8500) = 1.0000. $S_{PI}$ = \$200,000,000 at $SPLR_{PI}$ = 0.9000, $S_{D}$ = \$149,736,660 and $S_{E}$ = \$56,000,000 because $SPLR_{D}$ = 1.22434 and $SPLR_{D}$ = 2.2500. 

Large insurers such as $NHI$ and $B$ can cover all the losses they will incur with probability 0.9987 out of their current premium revenues. Small insurers cannot do this because they are more likely to have incurred losses that exceed the portion of their premiums available to pay losses. Small insurers should set aside large amounts of highly nliquid assets to meet the same solvency protection standards. 

\subsection{Aggregate Surplus By Portfolio Size}
\label{sec:AggregateSurplusByPortfolioSize}

Ideally, we want to insure all 309,000,000 Americans. Table~\ref{tab:InsurerOperatingResultsByPortfolioSize} Row 10 shows, the total Surplus needs, in Billions of dollars, by portfolio size. $NHI$ and $B$ can insure all Americans with \$0.00 aggregate Surplus, while 309 $PI$'s need \$61.8 Billion. But, 3,090 $D$'s need \$463 Billion, and 30,900 $E$'s need \$1.73 Trillion in unfunded Surplus to insurer every American. 

By ignoring small insurers', and risk assuming health care providers' Surplus needs, capitation advocates failed to address a significant flaw in capitation: small insurers (risk assuming health care providers) need Trillions of dollars in Surplus they have not been funding. Inadequately capitalized, risk assuming health care providers have been failing, clinically and financially, for decades \citep{Mayes2005}. In the aftermath of Hurricane Katrina, patients died because health care facilities were inadequately staffed and provisioned and could not continue to deliver care, despite having been paid, in advance, through capitation.

Before becoming health insurers, risk assuming health care providers should have diverted most, if not all, of their assets to capitalizing their impending, inefficient insurance operations. Had they done this, they would have become inefficient clinicians because Surplus assets can not be used to produce clinical services. It is only because risk assuming health care providers do not adequately capitalize their inefficient insurance operations that their capitation induced inefficiencies are not immediately apparent. Capitated providers are able to continue their inefficient and under-capitalized insurance operations because capitation advocates refuse to admit that capitation will not, and never could, work in efficient health care (finance) systems.

While daunting, the aggregate Surplus levels reported in Table~\ref{tab:InsurerOperatingResultsByPortfolioSize} are understated. Because $SPLR_{N}$ protects single insurers from insolvency, not all insurers, it is likely that at least one insurer will become insolvent. We should therefore use Bonferroni corrected \citep{HoggLossDist1984} aggregate surplus requirements for small insurers and risk assuming health care providers where the cited probabilityt of insolvency applies to all, these Bonferroni corrected surplus requirements are much higher than the amounts shown in Table~\ref{tab:InsurerOperatingResultsByPortfolioSize}.
%Risk assuming health care providers cannot possibly set aside sufficient surplus to meet their exposure to higher than average levels of demand for health care services that may occur during epidemics, natural catastrophes, or (wo)man-made disasters. If risk assuming health care providers do set aside sufficient surplus for their insurance risks, they become inefficient clinicians. If they fail to set aside sufficient surplus, they are highly likely to fail to meet the needs of their patients. Portfolio size adjusted surplus requirements pose a significant barrier to entry into the insurance business for small insurers, and insurmountable barriers to entry into the insurance business for health care providers. 